A privately owned liquor store operates both a drive-in facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint pdf of these random variables is as shown: f(x,y) =x+y when 0

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A privately owned liquor store operates both a drive-in facility and a walk-in facility. On a randomly selected day, let \(X\) and \(Y\), respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint probability density function (pdf) of these random variables is as shown:

\[ f(x,y) = x + y \] 

when \(0 < x < 1\) and \(0 < y < 1\) and 0 otherwise.

**Question:**
Are \(X\) and \(Y\) independent?
Transcribed Image Text:A privately owned liquor store operates both a drive-in facility and a walk-in facility. On a randomly selected day, let \(X\) and \(Y\), respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint probability density function (pdf) of these random variables is as shown: \[ f(x,y) = x + y \] when \(0 < x < 1\) and \(0 < y < 1\) and 0 otherwise. **Question:** Are \(X\) and \(Y\) independent?
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